How old will Jessica be when Dad carries out his promise?

Question

Dad said to my sister Jessica: "When you are one third as old as I am, I shall buy you new computer." Jessica is now 12 and Dad is 56. How old will Jessica be when Dad carries out his promise?

Answer 1

Hmmm. Let's add 10 years to their ages and see where we stand:

22 / 66 = ¹/₃

So she will be 22 years old.

 

Answer 2

Let x= the number of years until Jessica is 1/3 Dad's age.

3(x+12)=x+56

3x+36=x+56

2x=20

x=10

After 10 years, Jessica will be 22 and Dad will be 66.

 

To check for accuracy,

66/22=3.

 

So, when Jessica is 22, Dad will be 3x her age, and she will be one-third of Dad's age.

Answer 3

let x=# of years until Jessica is 1/3 as old as her dad

(12+x)=(1/3)(56+x)

12+x=56/3 + (1/3)(x)

x-(1/3)x=(56/3)-12

(2/3)(x)=18 2/3-12

(2/3)(x)=6 2/3

(2/3)(x)=20/3

multiply both sides by 3/2

(3/2)(2/3)(x)=(3/2)(20/3)

x=10 years (after simplifying-20/2=10 and the 3s cancel, or (3*20)/(2*3)=60/6=10)

Jessica will be 12+10=22 years old and her father will be 56+10=66 years old